tLaSDI: Thermodynamics-informed latent space dynamics identification
- URL: http://arxiv.org/abs/2403.05848v2
- Date: Fri, 22 Mar 2024 01:01:58 GMT
- Title: tLaSDI: Thermodynamics-informed latent space dynamics identification
- Authors: Jun Sur Richard Park, Siu Wun Cheung, Youngsoo Choi, Yeonjong Shin,
- Abstract summary: We propose a latent space dynamics identification method, namely tLa, that embeds the first and second principles of thermodynamics.
The latent variables are learned through an autoencoder as a nonlinear dimension reduction model.
An intriguing correlation is empirically observed between a quantity from tLa in the latent space and the behaviors of the full-state solution.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: We propose a latent space dynamics identification method, namely tLaSDI, that embeds the first and second principles of thermodynamics. The latent variables are learned through an autoencoder as a nonlinear dimension reduction model. The latent dynamics are constructed by a neural network-based model that precisely preserves certain structures for the thermodynamic laws through the GENERIC formalism. An abstract error estimate is established, which provides a new loss formulation involving the Jacobian computation of autoencoder. The autoencoder and the latent dynamics are simultaneously trained to minimize the new loss. Computational examples demonstrate the effectiveness of tLaSDI, which exhibits robust generalization ability, even in extrapolation. In addition, an intriguing correlation is empirically observed between a quantity from tLaSDI in the latent space and the behaviors of the full-state solution.
Related papers
- NeuralODEs for VLEO simulations: Introducing thermoNET for Thermosphere Modeling [4.868863044142366]
thermoNET represents thermospheric density in satellite orbital propagation using a reduced amount of differentiable computations.
Network parameters are learned based on observed dynamics, adapting through ODE sensitivities.
arXiv Detail & Related papers (2024-05-29T09:12:44Z) - Thermodynamics-informed super-resolution of scarce temporal dynamics data [4.893345190925178]
We present a method to increase the resolution of measurements of a physical system and subsequently predict its time evolution.
Our method uses adversarial autoencoders, which reduce the dimensionality of the full order model to a set of latent variables that are enforced to match a prior.
A second neural network is trained to learn the physical structure of the latent variables and predict their temporal evolution.
arXiv Detail & Related papers (2024-02-27T13:46:45Z) - Discovering Interpretable Physical Models using Symbolic Regression and
Discrete Exterior Calculus [55.2480439325792]
We propose a framework that combines Symbolic Regression (SR) and Discrete Exterior Calculus (DEC) for the automated discovery of physical models.
DEC provides building blocks for the discrete analogue of field theories, which are beyond the state-of-the-art applications of SR to physical problems.
We prove the effectiveness of our methodology by re-discovering three models of Continuum Physics from synthetic experimental data.
arXiv Detail & Related papers (2023-10-10T13:23:05Z) - Learning Neural Constitutive Laws From Motion Observations for
Generalizable PDE Dynamics [97.38308257547186]
Many NN approaches learn an end-to-end model that implicitly models both the governing PDE and material models.
We argue that the governing PDEs are often well-known and should be explicitly enforced rather than learned.
We introduce a new framework termed "Neural Constitutive Laws" (NCLaw) which utilizes a network architecture that strictly guarantees standard priors.
arXiv Detail & Related papers (2023-04-27T17:42:24Z) - Capturing dynamical correlations using implicit neural representations [85.66456606776552]
We develop an artificial intelligence framework which combines a neural network trained to mimic simulated data from a model Hamiltonian with automatic differentiation to recover unknown parameters from experimental data.
In doing so, we illustrate the ability to build and train a differentiable model only once, which then can be applied in real-time to multi-dimensional scattering data.
arXiv Detail & Related papers (2023-04-08T07:55:36Z) - ConCerNet: A Contrastive Learning Based Framework for Automated
Conservation Law Discovery and Trustworthy Dynamical System Prediction [82.81767856234956]
This paper proposes a new learning framework named ConCerNet to improve the trustworthiness of the DNN based dynamics modeling.
We show that our method consistently outperforms the baseline neural networks in both coordinate error and conservation metrics.
arXiv Detail & Related papers (2023-02-11T21:07:30Z) - Physics Informed RNN-DCT Networks for Time-Dependent Partial
Differential Equations [62.81701992551728]
We present a physics-informed framework for solving time-dependent partial differential equations.
Our model utilizes discrete cosine transforms to encode spatial and recurrent neural networks.
We show experimental results on the Taylor-Green vortex solution to the Navier-Stokes equations.
arXiv Detail & Related papers (2022-02-24T20:46:52Z) - Data-driven reduced order modeling of environmental hydrodynamics using
deep autoencoders and neural ODEs [3.4527210650730393]
We investigate employing deep autoencoders for discovering the reduced basis representation.
Test problems we consider include incompressible flow around a cylinder as well as a real-world application of shallow water hydrodynamics in an estuarine system.
arXiv Detail & Related papers (2021-07-06T17:45:37Z) - Gradient Starvation: A Learning Proclivity in Neural Networks [97.02382916372594]
Gradient Starvation arises when cross-entropy loss is minimized by capturing only a subset of features relevant for the task.
This work provides a theoretical explanation for the emergence of such feature imbalance in neural networks.
arXiv Detail & Related papers (2020-11-18T18:52:08Z) - OnsagerNet: Learning Stable and Interpretable Dynamics using a
Generalized Onsager Principle [19.13913681239968]
We learn stable and physically interpretable dynamical models using sampled trajectory data from physical processes based on a generalized Onsager principle.
We further apply this method to study Rayleigh-Benard convection and learn Lorenz-like low dimensional autonomous reduced order models.
arXiv Detail & Related papers (2020-09-06T07:30:59Z) - Deep learning of thermodynamics-aware reduced-order models from data [0.08699280339422537]
We present an algorithm to learn the relevant latent variables of a large-scale discretized physical system.
We then predict its time evolution using thermodynamically-consistent deep neural networks.
arXiv Detail & Related papers (2020-07-03T08:49:01Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.